Question

Consider steady incompressible flow of a Newtonian fluid over a horizontal flat plate, as shown in the figure. The boundary layer thickness is proportional to

• A. $x^{1/4}$
• B. $x^{1/2}$
• C. $x^{-1/2}$
• D. $x^{2}$

Hint:

Remember $\delta \sim 5\,x/\sqrt{Re_x}$ for the laminar Blasius boundary layer; thus $\delta\propto x^{1/2}$.

Answer 1

The Correct Option is B

Step 1: Use the Blasius similarity result for a laminar flat-plate boundary layer.
For steady, incompressible, Newtonian flow over a flat plate (no pressure gradient), the Blasius solution gives \[ \delta(x)\;\approx\;C\,\frac{x}{\sqrt{Re_x}} \text{with} Re_x=\frac{U_\infty x}{\nu},\ C\approx 5. \]
Step 2: Extract $x$-dependence.
\[ \delta(x)\ \propto\ \frac{x}{\sqrt{U_\infty x/\nu}} \ =\ \sqrt{\frac{\nu}{U_\infty}}\;x^{1/2}. \] Hence $\delta\propto x^{1/2}$. Final Answer: \[ \boxed{x^{1/2}} \]